Question Number 211453 by BaliramKumar last updated on 09/Sep/24 Answered by A5T last updated on 09/Sep/24 $$\mathrm{5}^{{a}} \equiv\mathrm{5}\left({mod}\:\mathrm{10}\right);\mathrm{11}^{{c}} \equiv\mathrm{1}\left({mod}\:\mathrm{10}\right) \\ $$$$\Rightarrow\mathrm{5}^{{a}} +\mathrm{11}^{{c}} \equiv\mathrm{6}\left({mod}\:\mathrm{10}\right) \\ $$$$\mathrm{7}^{{b}}…
Question Number 211455 by BaliramKumar last updated on 09/Sep/24 Answered by BHOOPENDRA last updated on 10/Sep/24 $${Second}\:{hand}\:{T}_{{s}} =\mathrm{60}\:{sec} \\ $$$${minute}\:{hand}\:{T}_{{m}} =\mathrm{3600}\:{sec} \\ $$$${angular}\:{velocity} \\ $$$$\omega=\frac{\mathrm{2}\pi}{{T}}\:\left({where}\:{T}\:{is}\:{time}\:{period}\right)…
Question Number 211443 by BaliramKumar last updated on 09/Sep/24 Answered by A5T last updated on 09/Sep/24 $${Note}\:{that}\:{n}\leqslant\mathrm{10}\:{and}\:{cannot}\:{be}\:{composite} \\ $$$$\Rightarrow{It}\:{remains}\:{to}\:{check}\:{for}\:{n}=\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{7} \\ $$$$\mathrm{2}^{\mathrm{2}} −\mathrm{1}=\mathrm{3};\mathrm{2}^{\mathrm{3}} −\mathrm{1}=\mathrm{7};\mathrm{2}^{\mathrm{5}} −\mathrm{1}=\mathrm{31};\mathrm{2}^{\mathrm{7}} −\mathrm{1}=\mathrm{127}…
Question Number 211445 by BaliramKumar last updated on 09/Sep/24 Answered by A5T last updated on 09/Sep/24 $$={last}\:{three}\:{digits}\:{of}\:\mathrm{345}×\mathrm{789}=\mathrm{205}\Rightarrow\left({b}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 211456 by BaliramKumar last updated on 09/Sep/24 Answered by A5T last updated on 09/Sep/24 $${max}\:{when}\:\mathrm{8}{cos}\theta−\mathrm{8}{sin}\theta{cos}\theta=\mathrm{0} \\ $$$$\Rightarrow{cos}\theta=\mathrm{0}\:{or}\:{sin}\theta=\mathrm{1}\Rightarrow{max}=\mathrm{8}×\mathrm{1}−\mathrm{4}×\mathrm{1}=\mathrm{4} \\ $$ Answered by mehdee1342 last…
Question Number 208506 by Tawa11 last updated on 17/Jun/24 What is the smallest number which must added to 9454351626 so that it will become divisible…
Question Number 207713 by efronzo1 last updated on 24/May/24 Answered by Berbere last updated on 24/May/24 $$\underset{{i}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}{x}_{{i}} ^{\mathrm{2}} =\mathrm{125}\Rightarrow{only}\:\mathrm{125}\:{number}\:\neq\mathrm{0}\:{at}\:{least} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\mathrm{125}} {\sum}}{x}_{{i}}…
Question Number 207436 by CrispyXYZ last updated on 15/May/24 $${a},\:{b}\in\mathbb{N}_{+} ,\:\frac{{b}+\mathrm{1}}{{a}}+\frac{{a}+\mathrm{1}}{{b}}\in\mathbb{Z}.\:\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\left({a},\:{b}\right)\leqslant\sqrt{{a}+{b}.} \\ $$ Commented by A5T last updated on 15/May/24 $${What}\:{is}\:{meant}\:{by}\:\left({a},{b}\right)? \\ $$…
Question Number 207423 by efronzo1 last updated on 14/May/24 $$\:\:\:\:\downharpoonleft\underline{\:} \\ $$ Answered by mr W last updated on 14/May/24 $${let}\:{a}_{{n}} ={b}_{{n}} +{k} \\ $$$${b}_{{n}+\mathrm{1}}…
Question Number 207060 by efronzo1 last updated on 05/May/24 $$\:\:\downharpoonleft\underline{\:} \\ $$ Commented by mr W last updated on 05/May/24 $${i}\:{think}\:{you}\:{mean}\:{a}_{{n}+\mathrm{2}} . \\ $$ Answered…